arXiv subjects

Emily Williams

Publications and source records attributed to Emily Williams.

7 recordsLinked to original sources

arXiv2026

Physics-informed traditional and generative Mori-Zwanzig-reduced models for multiscale systems

Model reduction via the Mori-Zwanzig (MZ) formalism is well understood for coarse-grained representations constructed from standard basis functions such as Fourier functions. We show that the same formalism can be used to build reduced-order models in bases discovered by physics-informed machine learning. The fluctuation-dissipation theorem (FDT) is used to close the resulting non-Markovian evolution equations for the expansion coefficients of the learned basis. We further introduce a complementary, generative closure model. Relative to the Markovian dynamics alone, both the MZ and generative closures substantially improve predictions of the filtered states.

math.NA↗

arXiv2026

The SPace-based InterFerometer Feasibility (SPIFF) Project: Enabling Future High-Resolution Astronomy Across the EM Spectrum

A plethora of astronomical science cases can only be achieved with high angular resolution observations, and we can expect the number of these to grow as astronomers are constrained by the size limitations of single-aperture space telescopes, making space-based interferometry inevitable. However, the enabling technologies do not have flight heritage at the system level, and the concept remains immature to much of the community, meaning no direct-detection synthetic-aperture space-based interferometer has yet flown and an opportunity exists for the UK to take a world leading role. Here we propose the SPace-based InterFerometry Feasibility (SPIFF) Project as a program to address both issues simultaneously by: 1) completing a thorough survey of the science cases across the EM spectrum that would directly benefit from, or be impossible without, space-based interferometry; 2) down selecting key requirements via a Science Traceability Matrix mapping exercise; 3) host a workshop for the UK astronomical community to consolidate these findings; 4) build a technology demonstration mission to raise TRL and achieve flight heritage of critical technologies. Such a program positions the UK as the partner of choice for any future NASA or ESA space-based interferometry mission, allowing the UK to lead groundbreaking scientific discoveries, while also directly benefiting the UK industrial base by advancing domestic exportable technologies and building direct synergy with other UK space priorities. Indeed, the UK is uniquely positioned to lead in space-based interferometry, possessing a rare trifecta of domestic strengths: world-class expertise in ground-based interferometry and space-based instrumentation; commercial entities developing mission-critical technologies; and scientists whose research spans the full range of science cases that would benefit directly from space-based interferometry.

astro-ph.IM↗

arXiv2025

Stochastic generative methods for stable and accurate closure modeling of chaotic dynamical systems

Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in climate science and ocean modeling motivates the use of stochastic SGS models for chaotic dynamics. Further, developing stochastic generative models of underlying dynamics is a rapidly expanding field. In this work, we aim to incorporate stochastic integration toward closure modeling for chaotic dynamical systems. Further, we want to explore the potential stabilizing effect that stochastic models could have on linearized chaotic systems. We propose parametric and generative approaches for closure modeling using stochastic differential equations (SDEs). We derive and implement a quadratic diffusion model based on the fluctuations, demonstrating increased accuracy from bridging theoretical models with generative approaches. Results are demonstrated on the Lorenz-63 dynamical system.

math.NA↗

arXiv2024

What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what is being learned by physics-informed DeepONets by assessing the universality of the extracted basis functions and demonstrating their potential toward model reduction with spectral methods. Results provide clarity about measuring the performance of a physics-informed DeepONet through the decays of singular values and expansion coefficients. In addition, we propose a transfer learning approach for improving training for physics-informed DeepONets between parameters of the same PDE as well as across different, but related, PDEs where these models struggle to train well. This approach results in significant error reduction and learned basis functions that are more effective in representing the solution of a PDE.

cs.LG↗

arXiv2023

Near-Field Wall-Modeled Large-Eddy Simulation of the NASA X-59 Low-Boom Flight Demonstrator

Wall-modeled large-eddy simulation (WMLES) is utilized to analyze the experimental aircraft X-59 Quiet SuperSonic Technology (QueSST) developed by Lockheed Martin at Skunk Works for NASA's Low-Boom Flight Demonstrator project. The simulations utilize the charLES solver and aim to assess the ability of WMLES to predict near-field noise levels under cruise conditions, considering various subgrid-scale (SGS) models and grid resolutions. The results are compared with previous numerical studies based on the Reynolds-averaged Navier-Stokes (RANS) equations. Our findings demonstrate that WMLES produces near-field pressure predictions that are similar to those of RANS simulations at a comparable computational cost. Some mild discrepancies are observed between the WMLES and RANS predictions downstream the aircraft. These differences persist for finest grid refinement considered, suggesting that they might be attributed to underresolved interactions of shock waves and expansions waves at the trailing edge.

physics.flu-dyn↗

arXiv2022

Wall-modeled large-eddy simulation based on building-block flows

A unified subgrid-scale (SGS) and wall model for large-eddy simulation (LES) is proposed by devising the flow as a collection of building blocks that enables the prediction of the eddy viscosity. The core assumption of the model is that simple canonical flows contain the essential physics to provide accurate predictions of the SGS tensor in more complex flows. The model is constructed to predict zero-pressure-gradient wall-bounded turbulence, adverse pressure gradient effects, separation and laminar flow. The approach is implemented using a Bayesian classifier, which identifies the contribution of each building block in the flow, and a neural-network-based predictor, which estimates the eddy viscosity based on the building-block units. The training data are directly obtained from wall-modeled LES with an exact SGS/wall model for the mean quantities to guarantee consistency with the numerical discretization. The model is validated in canonical flows and the NASA High-Lift Common Research Model and shown to improve the predictions with respect to current modeling approaches.

physics.flu-dyn↗

arXiv2017

Thermal elastic-wave attenuation in low-dimensional SiN$_{x}$ bars at low temperatures

At low temperatures, < 200 mK, the thermal flux through low-dimensional amorphous dielectric bars, < 2 $μ$m wide and 200 nm thick, is transported by a small number of low-order elastic modes. For long bars, L > 400 $μ$m, it is known that the conductance scales as 1/L, where L is the length, but for short bars, 1 $μ$m < L < 400 $μ$m, the length dependence is poorly known. Although it is assumed that the transport must exhibit a diffusive to ballistic transition, the functional form of the transition and the scale size over which the transition occurs have not, to our knowledge, been measured. In this paper, we use ultra-low-noise superconducting Transition Edge Sensors (TESs) to measure the heat flux through a set of SiN$_{x}$ bars to establish the characteristic scale size of the ballistic to diffusive transition. For bars supporting 6 to 7 modes, we measure a thermal elastic-wave attenuation length of 20 $μ$m. The measurement is important because it sheds light on the scattering processes, which in turn are closely related to the generation of thermal fluctuation noise. Our own interest lies in creating patterned phononic filters for controlling heat flow and thermal noise in ultra-low-noise devices, but the work will be of interest to others trying to isolate devices from their environments, and studying loss mechanisms in micro-mechanical resonators.

cond-mat.mes-hall↗